In 19-24, use the RSA cipher from Examples 8.4.9 and 8.4.10. In 19-21, teranslate the message into its numeric equivalent and encrypt it. In 22-24, decrypt the ciphertext and translate the result in to letters of the alphabet to discover the message.

HeLLO

Write the message into its numeric and encrypt it.

Given information:

The given message is “HELLO”.

Formula used:

Division algorithm:

Let a be an integer and d be a positive integer. Then, there are unique integers q and r with 0≤r<d such that a=dq+r, here, q is the quotient and r is the remainder.

So, q=a div d and r=amodd.

RSA Cipher Work:

The formula of the RSA cryptography is C=Memodpq.

The numeric values of the letters HELLO are:

H=08,E=05,L=12,L=12,O=15

To encrypt the letters, use the formula C=Memodpq   …… (1)

Where, e=3 and pq=55.

To encrypt H, substitute 8 for H in the equation (1).

C=83mod55=512mod55=17    [512=9×55+17]

To encrypt E, substitute 5 for E in the equation (1)